#109:Infinite Series

The architects of Perplex City's railroads loved building
everything in straight lines - mountains, rivers, valleys -
none of it mattered to them. There's still one stretch west
of the city that continues for 100km with practically no
turns.

Imagine there are two trains travelling towards each other at either end of the 100km stretch at 50km/h.
Flying back and forth directly between the two trains at 75km/h is a bee that starts on the front of one
of the trains when they're 100km apart, and immediately turns around to the other train as soon as it reaches
it, and so on. How far will the bee have travelled in this zig zag fashion before the two trains meet?